Positive Solutions for Some Competitive Fractional Systems in Bounded Domains
Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Diric...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/140130 |
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| Summary: | Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some
Dirichlet conditions, where 0<α<2, σ,β≥1,s,r≥0. The potential functions p,q are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions Kα(D). |
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| ISSN: | 0972-6802 1758-4965 |